CollegePak Company produced and sold 60,000 backpacks during the year just ended at an average price of $20 per unit. Variable manufacturing costs were $8 per unit, and variable marketing costs were $4 per unit sold. Fixed costs amounted to $180,000 for manufacturing and $72,000 for marketing. There was no year-end work-in-process inventory. (Ignore income taxes.)
1. Compute CollegePak's break-even point in sales dollars for the year.
2. Compute the number of sales units required to earn a net income of $180,000 during the year.
3. CollegePak's variable manufacturing costs are expected to increase by 10 percent in the coming year. Compute the firm's break-even point in sales dollars for the coming year.
4. If CollegePak's variable manufacturing costs do increase by 10 percent, compute the selling price that would yield the same contribution-margin ratio in the coming year.
To answer these questions, we need to calculate the various components involved. Let's take them step by step:
1. Compute CollegePak's break-even point in sales dollars for the year.
The formula to calculate the break-even point in sales dollars is:
Break-even Point (in units) = Fixed Costs / Contribution Margin Ratio
Contribution Margin Ratio = (Selling Price per Unit - Variable Costs per Unit) / Selling Price per Unit
Variable Costs per Unit = Variable Manufacturing Costs per Unit + Variable Marketing Costs per Unit
Given information:
- Fixed Manufacturing Costs = $180,000
- Fixed Marketing Costs = $72,000
- Variable Manufacturing Costs per Unit = $8
- Variable Marketing Costs per Unit = $4
- Average Selling Price per Unit = $20
Calculations:
Variable Costs per Unit = $8 + $4 = $12
Contribution Margin Ratio = ($20 - $12) / $20 = $8 / $20 = 0.4
Fixed Costs = Fixed Manufacturing Costs + Fixed Marketing Costs
= $180,000 + $72,000 = $252,000
Break-even Point (in units) = $252,000 / 0.4 = $630,000
Therefore, CollegePak's break-even point in sales dollars for the year is $630,000.
2. Compute the number of sales units required to earn a net income of $180,000 during the year.
To calculate the number of sales units required to earn a net income, we can use the following formula:
Net Income = (Sales Units × Contribution Margin per Unit) - Fixed Costs
Given information:
- Net Income = $180,000
- Contribution Margin per Unit = Selling Price per Unit - Variable Costs per Unit = $20 - $12 = $8
- Fixed Costs = $252,000 (from the previous calculation)
Calculations:
$180,000 = (Sales Units × $8) - $252,000
$180,000 + $252,000 = Sales Units × $8
$432,000 = Sales Units × $8
Sales Units = $432,000 / $8
Sales Units = 54,000 units
Therefore, CollegePak would need to sell 54,000 units to earn a net income of $180,000 during the year.
3. CollegePak's variable manufacturing costs are expected to increase by 10 percent in the coming year. Compute the firm's break-even point in sales dollars for the coming year.
To compute the break-even point in sales dollars for the coming year, we need to consider the increase in variable manufacturing costs by 10 percent.
New Variable Manufacturing Costs per Unit = Variable Manufacturing Costs per Unit + (Variable Manufacturing Costs per Unit × 10%)
Given information:
- Variable Manufacturing Costs per Unit = $8
Calculations:
New Variable Manufacturing Costs per Unit = $8 + ($8 × 10%) = $8 + ($8 × 0.1) = $8 + $0.8 = $8.8
Variable Costs per Unit = $8.8 + $4 = $12.8
New Break-even Point (in units) = Fixed Costs / Contribution Margin Ratio
= $252,000 / (($20 - $12.8) / $20)
= $252,000 / ($7.2 / $20)
= $252,000 / (0.36)
= $700,000
Therefore, CollegePak's break-even point in sales dollars for the coming year is $700,000.
4. If CollegePak's variable manufacturing costs do increase by 10 percent, compute the selling price that would yield the same contribution-margin ratio in the coming year.
To calculate the selling price that would yield the same contribution-margin ratio, we need to consider the increase in variable manufacturing costs and maintain the same contribution-margin ratio.
Contribution Margin Ratio = (Selling Price per Unit - Variable Costs per Unit) / Selling Price per Unit
Given information:
- New Variable Manufacturing Costs per Unit = $8.8 (from the previous calculation)
- Variable Marketing Costs per Unit = $4
Calculations:
Contribution Margin Ratio = (Selling Price per Unit - Variable Costs per Unit) / Selling Price per Unit
0.4 = (Selling Price per Unit - ($8.8 + $4)) / Selling Price per Unit
0.4 = (Selling Price per Unit - $12.8) / Selling Price per Unit
Let's assume Selling Price per Unit is SP.
0.4 = (SP - $12.8) / SP
0.4SP = SP - $12.8
0.4SP - SP = -$12.8
0.6SP = $12.8
SP = $12.8 / 0.6
SP = $21.33 (rounded to the nearest cent)
Therefore, the selling price that would yield the same contribution-margin ratio, if CollegePak's variable manufacturing costs increase by 10 percent, is approximately $21.33.
1. To compute CollegePak's break-even point in sales dollars for the year, we need to determine the total fixed costs and the contribution margin ratio.
The total fixed costs include both manufacturing and marketing fixed costs, which amount to $180,000 + $72,000 = $252,000.
The contribution margin ratio is calculated as follows:
Contribution margin ratio = (Sales price per unit - Variable costs per unit) / Sales price per unit
Sales price per unit is $20, variable manufacturing costs per unit are $8, and variable marketing costs per unit sold are $4. So, the contribution margin per unit is $20 - $8 - $4 = $8.
Using the contribution margin ratio formula:
Contribution margin ratio = $8 / $20 = 0.4 or 40%.
The break-even point in sales dollars is then calculated by dividing the total fixed costs by the contribution margin ratio:
Break-even point = Total fixed costs / Contribution margin ratio
Break-even point = $252,000 / 0.4
Break-even point = $630,000
Therefore, CollegePak's break-even point in sales dollars for the year is $630,000.
2. To compute the number of sales units required to earn a net income of $180,000 during the year, we need to consider the contribution margin per unit and the desired net income.
The contribution margin per unit is $8, as calculated earlier. Therefore, to earn a net income of $180,000, we need to cover the fixed costs and have the remaining amount as net income.
Net income = (Number of units sold) x (Contribution margin per unit) - Fixed costs
Since we want the net income to be $180,000, we can rearrange the equation as follows:
(Number of units sold) x (Contribution margin per unit) = Fixed costs + Net income
(Number of units sold) x $8 = $252,000 + $180,000
(Number of units sold) = ($252,000 + $180,000) / $8
(Number of units sold) = $432,000 / $8
(Number of units sold) = 54,000 units
Therefore, CollegePak would need to sell 54,000 units to earn a net income of $180,000 during the year.
3. Considering that CollegePak's variable manufacturing costs are expected to increase by 10 percent in the coming year, we can calculate the new contribution margin per unit and then determine the break-even point in sales dollars for the coming year.
With a 10 percent increase in variable manufacturing costs, the new variable manufacturing cost per unit would be $8 + ($8 * 0.10) = $8 + $0.80 = $8.80.
The contribution margin per unit would then be:
Contribution margin per unit = Sales price per unit - Variable costs per unit
Contribution margin per unit = $20 - $8.80 = $11.20
To find the break-even point in sales dollars for the coming year, we would use the same equation as before:
Break-even point = Total fixed costs / Contribution margin ratio
The contribution margin ratio remains unchanged since it is calculated based on the sales price and variable costs per unit. Using the values from the previous calculation:
Break-even point = $252,000 / 0.4
Break-even point = $630,000
Therefore, even with a 10 percent increase in variable manufacturing costs, CollegePak's break-even point in sales dollars for the coming year remains the same at $630,000.
4. If CollegePak's variable manufacturing costs increase by 10 percent, we need to compute the selling price that would yield the same contribution-margin ratio in the coming year.
The contribution margin ratio is given by:
Contribution margin ratio = (Selling price per unit - Variable costs per unit) / Selling price per unit
Let's assume the new selling price per unit is SP. The new variable manufacturing cost per unit would be $8 + ($8 * 0.10) = $8 + $0.80 = $8.80. Therefore, the contribution margin per unit would be:
Contribution margin per unit = SP - $8.80
We want the same contribution margin ratio as before, so we have:
0.4 = (SP - $8.80) / SP
We can now solve for SP:
0.4SP = SP - $8.80
0.4SP - SP = -$8.80
-0.6SP = -$8.80
SP = (-$8.80) / (-0.6)
SP = $14.67 (rounded to the nearest cent)
Therefore, if CollegePak's variable manufacturing costs increase by 10 percent, the selling price that would yield the same contribution-margin ratio in the coming year is approximately $14.67.
Activity
1. $630,000
2. 54,000 units
3. $ 600,000
4. $32